The Boundary Element Method for Acoustic Transmission with Nonconforming Grids

TL;DR

This paper introduces a boundary element method that uses nonconforming grids at material interfaces, enhancing computational efficiency and flexibility for acoustic transmission problems, especially at high frequencies and contrasts.

Contribution

It develops a nonconforming boundary element algorithm that allows independent surface mesh generation, improving efficiency and adaptability in acoustic transmission simulations.

Findings

Significant reduction in computational cost with nonconforming grids.

Effective for various boundary integral formulations and coupling methods.

Validated through extensive benchmarks and acoustic foam models.

Abstract

Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at high frequencies due to the increase in mesh size with a fixed number of elements per wavelength and also at high material contrasts due to the ill-conditioning of the linear system. This study presents the design of boundary element methods feasible for nonconforming surface meshes at the material interface. The nonconforming algorithm allows for independent grid generation, improves flexibility, and reduces the degrees of freedom. It works for different boundary integral formulations for Helmholtz transmission problems, operator preconditioning, and coupling with finite element solvers. The extensive numerical benchmarks at canonical configurations and an acoustic foam model confirm the significant improvements in computational efficiency when employing the nonconforming grid coupling in the boundary element method.